The Hammers appear to be on the brink of agreeing a deal to move into the £429million venue after co-chairman David Gold revealed earlier this month that discussions could conclude as early as Saturday.
While any switch would not take place until 2016, Hurst believes it could entice the sort of foreign investment that has catapulted Manchester City and Chelsea into Europe's elite.
The Hammers have been one of the sleeping giants of English football since the likes of Hurst, Sir Trevor Brooking and Bobby Moore graced Upton Park in the 1960s.
And with a supporter base to match the likes of City and Chelsea, the 71-year-old thinks a new golden generation could be triggered.
"It's not beyond the realms of possibility if we go to the stadium and with the support we've got," said Hurst.
"West Ham has a huge supporter base. If you could make a comparison to another club of a similar stature and I would say Manchester City is it.
"Look what has happened to them after they went to a new stadium.
"If you were a foreign investor looking to buy a football club then West Ham would be a similar contender in the new stadium.
"More so if you want to buy a London club rather than a team in Manchester.
"It would be absolutely unbelievable. That could happen.
"I think it has been great for Chelsea with (Roman) Abramovich and for Manchester City. It has been great for the game. Of course I'd be thrilled to bits if it happened to West Ham."
Any move would, however, end a century-long existence at the Boleyn Ground.
Some Hammers fans have therefore been reticent to back a move away and, while Hurst sympathises, he believes the club would lose too much by ignoring the possibilities in Stratford.
"I do strongly believe that for the club to move forward we need to move to a bigger stadium," he said.
"Nobody has a greater connection to Upton Park than I have as a player or a fan. I've had some great days and I have a great connection with the club.
"I firmly believe it (moving to the Olympic Park) is the future for us. We need to be there."
In the short-term Hurst believes one of the most important decision for the club is ensuring manager Sam Allardyce remains.
Allardyce's contract runs out at the end of the season with contractual talks not due to begin until the summer.
The club have suggested the delay has been deliberate so that both parties can go into negotiations aware of which division they will play in next term.
But with safety almost assured - the Hammers sit 12th and nine points clear of danger - Hurst is hopeful Allardyce will be given a new deal.
"I'd like to think for the sake of continuity he'll stay on," he said.
"I don't know the background. People are saying that at this stage they should be talking but there are issues.
"The first is that it remains to be seen if they stay in the top flight. If they stay in the top flight, which they look like doing, then I'd be the first to say carry on Sam.
"Most West Ham fans would have said if we can stay out of the bottom three at the start of the year then we'd be happy.
"Here we are lingering mid-table which we've looked like doing all season with a limited squad and restrictions including injuries to some players in key positions.
"I do hope he continues."